1hill1.mac and hill2.mac are from the book "Computer Algebra in Applied
2Mathematics: An introduction to MACSYMA", by Richard H Rand, Pitman
3(1984).
4
5Mathieu's equation is x''+(delta+e*cos(t))*x=0
6
7For given values of the parameters delta and e, either all the
8solutions are bounded (the equation is stable) or there exist
9unbounded solutions (the equation is unstable).  The regions of
10stability are separated from thos of instability by "transition
11curves".
12
13This program computes the transition curves of Mathieu's equation
14using Fourier series to obtain Hill's determinants.
15
16The run below, using maxima-5.9.0cvs, reproduces the result on pages
17108-109 of the book.  The results are identical to those from
18mathieu0.mac and mathieu.mac.
19
20
21(C1) load("./hill1.mac");
22(D1)                              ./hill1.mac
23(C2) load("./hill2.mac");
24(D2)                              ./hill2.mac
25(C3) hill();
26ENTER TRANSITION CURVE NUMBER N
270;
28ENTER DEGREE OF TRUNCATION
296;
30             6      4    2
31         29 e    7 e    e
32delta= - ----- + ---- - --
33          144     32    2
34
35(D3)                                 FALSE
36(C4) hill();
37ENTER TRANSITION CURVE NUMBER N
381;
39ENTER DEGREE OF TRUNCATION
406;
41           6       5    4     3    2
42       49 e    11 e    e     e    e    e   1
43delta= ----- - ----- - --- + -- - -- - - + -
44       36864   4608    384   32   8    2   4
45
46           6       5    4     3    2
47       49 e    11 e    e     e    e    e   1
48delta= ----- + ----- - --- - -- - -- + - + -
49       36864   4608    384   32   8    2   4
50
51(D4)
52(C5) hill();
53ENTER TRANSITION CURVE NUMBER N
542;
55ENTER DEGREE OF TRUNCATION
566;
57                6        4      2
58       1002401 e    763 e    5 e
59delta= ---------- - ------ + ---- + 1
60        4976640      3456     12
61
62              6       4    2
63         289 e     5 e    e
64delta= - ------- + ---- - -- + 1
65         4976640   3456   12
66
67
68
69Local Variables: ***
70mode: Text ***
71End: ***